Wednesday 20 March 2013 h. 16:00, room 2BC30

Silvia GAZZOLA (Padova, Dip. Mat.)

"Regularization techniques for linear inverse ill-posed problems"

Abstract

Inverse problems are ubiquitous in many areas of science and engineering: they are typically modeled by Fredholm integral equations of the first kind and the available data are commonly affected by errors. Once discretized they give rise to ill-conditioned linear systems, often of huge dimensions: regularization consists in replacing the original system by a nearby problem with better numerical properties, in order to find a meaningful approximation of the exact solution.

During this talk we will focus on problems regarding the restoration of images corrupted by blur and noise. We will review some standard regularization methods, both direct and iterative, and we will introduce the most recent class of the Arnoldi-Tikhonov methods. The results of many numerical experiments will be shown, so to compare the different approaches and to contribute validating the newly-proposed strategies.

Rif. int. C. Marastoni, T. Vargiolu